What is the integral of ((x^2))/2-8x+30 ?

The integral of ((x^2))/2-8x+30 is (x^3)/6-4x^2+30x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((x^2))/2-8x+30

\int \frac{( x ^{2} )}{2} - 8 x + 30 d x

\frac{x ^{3}}{6} - 4 x^{2} + 30 x + C

Solution steps

\int \frac{x ^{2}}{2} - 8 x + 30 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{x ^{2}}{2} d x - \int 8 x d x + \int 30 d x

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

\int 8 x d x = 4 x^{2}

\int 30 d x = 30 x

= \frac{x ^{3}}{6} - 4 x^{2} + 30 x

Add a constant to the solution

= \frac{x ^{3}}{6} - 4 x^{2} + 30 x + C

\int e^{x} + 12 x^{2} - 4 d x

\int \frac{1}{( 4 x ^{2} - 24 x + 27 ) ^{3}} d x

\int 3 x^{2} (x^{3} - 5)^{4} d x

\int 4 x^{2} - 5 x d x

\int \frac{1}{( x ( x ^{2} + 1 ) )} d x

What is the integral of ((x^2))/2-8x+30 ?
The integral of ((x^2))/2-8x+30 is (x^3)/6-4x^2+30x+C